### Explicitly covariant form of the integral Maxwell equations

#### Abstract

It is analyzed in detail the covariance of the integral forms of the Maxwell Equations. Different forms of writing the integral Maxwell equations in explicitly covariant form are analyzed. First we show how one of these ways can be obtained from the differential Maxwell equations, both from their usual three vector form as from their covariant four vector form. Then we discuss how this covariant integral Maxwell equations can be obtained from usual integral Maxwell equations. It is emphasized the necessity to write the usual integral equations without time derivatives. The integrations regions in the three-dimensional space and time are identified with parts of the same hyper-surface in four-dimensional space-time. This point is carefully analyzed. Later we discuss other forms of the integral Maxwell equations. We show how these new versions can be expressed in an explicitly covariant form.

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DOI: https://doi.org/10.31349/RevMexFisE.18.76

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**REVISTA MEXICANA DE FÍSICA E**, year 18, issue 1, January-June 2021. Semiannual Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf-e, rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216402500-203, **ISSN: 2683-2216 (on line), 1870-3542 (print)**, both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, January 04, 2021.

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